The union representing Air Canada flight attendants says it will continue to defy a back-to-work order despite the Canada Industrial Relations Board ruling their strike "unlawful".

The independent federal tribunal deemed the job action by the cabin crews - now in its third day - illegal on Monday after the union defied a government back-to-work order issued over the weekend.

"If Air Canada thinks planes will be flying this afternoon, they're sorely mistaken," said Canadian Union of Public Employees president Mark Hancock.

The strike by more than 10,000 flight attendants for Canada's largest airline has stranded tens of thousands of passengers since flights were grounded on Saturday.

Air Canada has not yet responded to the union's latest move. (BBC)